Problem Solving

Question

A certain tank has an inlet valve and an outlet valve. The tank can be filled via the inlet valve in 6 minutes and emptied (from full) via the outlet valve in 10 minutes. If both valves were operating, how long would it take to fill the tank if it was empty to begin with?

Answer 1

1/6 = portion of tank filled by inlet valve per minute

 

1/10 = portion of tank emptied by outlet valve per minute

 

Let x = number of minutes it takes to fill the tank if both valves are operational

 

1/x = portion filled by both valves per minute

 

Then 1/6 - 1/10 = 1/x

 

Multiply by the LCD, 30x, to obtain:  5x - 3x = 30

 

                                                            2x = 30

 

                                                              x = 15 minutes

 

Answer 2

t represents the time both are open

 

6/t + t/10 = 1

 

Can you solve for t and answer?